Toni Ikonen

activity

20242026

collaborators

9 papers

math.MG2026

Quasihyperbolic domains are CAT(2)

Toni Ikonen, Abhishek Pandey

We prove that every proper subdomain of the Euclidean space equipped with its quasihyperbolic metric is CAT(2). The CAT property leads to a positive resolution of Väisälä's uniquen…

math.DG2026

A rescaling principle for quasiregular curves with applications to hyperbolicity

Toni Ikonen, Jonathan Pim

We prove a Miniowitz--Zalcman rescaling principle for quasiregular curves into calibrated manifolds. We have two main applications. First, we introduce Brody hyperbolicity adapted…

math.DG2026

Sobolev-to-Lipschitz property of geodesically complete spaces with curvature bounded from above

Emanuele Caputo, Nicola Cavallucci, Toni Ikonen

We prove that every length space with curvature bounded from above that is geodesically complete has the Sobolev-to-Lipschitz property with exponent infinity. That is, every Sobole…

math.DG2026

Ultralimits of Sobolev maps and stability of Dehn functions

Toni Ikonen, Stefan Wenger

We show that the ultralimit of a bounded sequence of Lipschitz maps into pointed metric spaces extends naturally to $p$ -bounded sequences of Sobolev maps and that this ultralimit f…

math.DG2025

Entire conformal curves are affine or have super-Euclidean energy growth

Toni Ikonen

We prove that entire conformal curves $R^{n} \to R^{m}$ fall into two classes: either the curve is affine or the average energy in a ball is strictly increasi…

math.MG2025

On infinity thick quasiconvexity and applications

Miguel García-Bravo, Toni Ikonen, Zheng Zhu

We investigate geometric properties of a metric measure space where every function in the Newton--Sobolev space $N^{1, \infty} (Z)$ has a Lipschitz representative. We prove that when…

math.DG2025

Smooth contact lifts to central extensions of Carnot groups

Eero Hakavuori, Susanna Heikkilä, Toni Ikonen

We consider the existence problem of lifting a smooth contact map between Carnot groups to a smooth contact map between central extensions of the original groups. Our main result i…

math.DG2024

Liouville's theorem in calibrated geometries

Toni Ikonen, Pekka Pankka

We consider the following extension of the classical Liouville theorem: A calibration $ω \in Λ^{n} R^{m}$ , where $3 \leq n \leq m$ , has the Liouville property if a Sobolev mappin…

math.DG2024

Quasiregular curves: Removability of singularities

Toni Ikonen

We prove a Painlevé theorem for bounded quasiregular curves in Euclidean spaces extending removability results for quasiregular mappings due to Iwaniec and Martin. The theorem is p…